How do you simplify #(30x^2+ 2x) /( x^2+x-2 ) *( (x+2)(x-2))/(15x^3-30x^2)#?
1 Answer
Explanation:
Your starting expression is
#(30x^2 + 2x)/(x^2 + x - 2) * ((x+2)(x-2))/(15x^3 - 30x^2)#
Your first step is to try and simplify the numerators and denominators as much as possible by factoring them.
#30x^2 + 2x = 2x(15x + 1)#
#x^2 + x - 2 = x^2 + 2x - x - 2#
#=x(x+2) - (x+2)#
#=(x+2)(x-1)#
and
#15x^3 - 30x^2 = 15x^2(x-2)#
The expression can thus be rewritten as
#(2x(15x+1))/((x+2)(x-1)) * ((x+2)(x-2))/(15x^2(x-2))#
Notice that the expressions that can be found both in the numerator, and in the denominator cancel out to give
#(2x(15x+1))/(color(red)(cancel(color(black)((x+2))))(x-1)) * (color(red)(cancel(color(black)((x+2))))color(blue)(cancel(color(black)((x-2)))))/(15x^2color(blue)(cancel(color(black)((x-2)))))#
You are left with
#(2color(purple)(cancel(color(black)(x)))(15x+1))/(x-1) * 1/(15x * color(purple)(cancel(color(black)(x)))) = color(green)( (2(15x+1))/(15x(x-1))#
